"instead of deleting files, we'd like to hide them"
I think that we are speaking of records, not files.
The Omit command makes what it says: omit one ( or more ) record from the found set.
When it's time to export, only the found set ( total of NOT omitted records ) will be exported.
Are you asking about the "Omit" function when finding records or using the Omit Records option to hide records from the current found set?
Filemaker allows you to organize the records of a specific table into two groups. One group is called the Found Set and these are the records currently visible on a given layout. All the records that are not in the found set (Sometimes called the "omitted" set) represent the second group.
Omit Record (only in Browse mode) moves the current record from the found set to the omitted set. Find All and Show Omitted are two other tools for working with these two record groups. Show All Records followed by Show Omitted Records, for example, will give you a found set of zero records as all records have been moved into the Omitted set.
When you print or PDF a report, the records in the found set of the current layout will be displayed in that report. The records from the omitted set will not be. If your reports are displaying records that you do not want to see, your found set must have records you do not want.
The omit option when used in find mode, says "omit all records that don't match this criteria from the found set". If you are using the Omit option while finding records, make sure that the Omit requests are set up after any regular find requests.
Example: You want to find all records where first name is George but last name is NOT Washington
Enter find mode
Type George in the first name field.
Select New Request to start a second find request
Click the Omit button and enter Washington in the last name field.
Perform the find.
Hope that helps.